In mathematics, and more specifically in graph theory, a polytree[1] (also called directed tree,[2] oriented tree[3] or singly connected network[4]) is a directed acyclic graph whose underlying undirected graph is a tree. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is both connected and acyclic. (It is required that no two undirected edges are replaced by the same directed edge; i.e. there must be no pair of vertices linked in the directed graph by edges in both directions.)
A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is acyclic.
A polytree is an example of an oriented graph.
The term polytree was coined in 1987 by Rebane and Pearl.[5]